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CT Publications
Surviving Maths
in AS Biology by
Dr Robert Mitchell
www.SurvivingMathsInASBiology.co.uk
A catalogue record for this book is available from the British Library
ISBN 978-1-907769-02-3
First published in September 2010 by
CT Publications
Copyright © Dr Robert Mitchell 2010
The right of Robert Mitchell to be identified as the author of this work has been asserted by
him in accordance with the Copyright and Designs and Patents Act 1988. All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording or any information storage and
retrieval system, without permission in writing from the publisher at the address below.
Published by
CT Publications*
40 Higher Bridge Street
Bolton
Greater Manchester
BL1 2HA
First printing September 2010
10 9 8 7 6 5 4 3 2 1
*CT Publications is owned by Chemistry Tutorials located at the same address.
Contents
Acknowledgements
I would like to thank Denise for her infinite patience, her reading and proofing
skills and having the unending ability to encourage and support the production of
this work. Thanks also to my Mum, Joyce and Brother, Colin for just being
there.
About the author
Rob is a private tutor in chemistry and biology in Bolton. He’s formerly worked in
medical research as technician, research assistant and post-doctoral researcher
and has contributed to the publication of over 40 research papers. During a
varied career in science, he’s been a project leader in industry, a lecturer and
examiner and blogs daily as Chemicalguy. He likes dogs, and pies, going to the
movies and walking!
Other books by the author
AQA A2 Biology; Writing the Synoptic Essay May 2010
Surviving Maths in AS Chemistry August 2010
Ultimate Exam Preparation; AQA Chemistry Unit 1 October 2010 (in press)
Ultimate Exam Preparation; AQA Biology Unit 1 November 2010 (in press)
Biofuelishness (Popular Science) December 2010 (in press)
Frequency tables, pie charts, bar charts and histograms
A frequency table, or tally chart is a means of collecting and organising data
into discrete groups. The data is then often presented as a bar chart or
histogram. Tally charts for sampling biological data usually have two or
more columns, the first of which is for recording the independent variable. If
the independent variable can be numbered (like a weight, height etc) it is
quantitative), if cannot be numbered it is said to be qualitative (like brown
eyes, blue eyes etc).
Categoric data If we were to make a frequency table for animals in a farmer’s field we might
list the different animals in the first column and tally the number (or
frequency) of that animal in the second column. Because the animals fall
into different categories that do not overlap, the data is said to be categoric
and discontinuous. As they aren’t numbers, the data is said to be
qualitative.
Animal Frequency Cow 25 Pig 15
Chicken 48 Horse 4
Escapee from prison 2
Such data can be presented on a pie or bar chart. The pie chart represents
the total number of animals as 100%, and is the entire 3600 of the circle.
Each variable is then attributed a slice of the pie whose size is proportional
to the frequency, so the more it is then the bigger the slice. In the example
below, 48 out of 94 animals are chickens and so their slice of the pie is just
over a half at 51%, or 183.80 and so on for the rest of the animals.
Cow, 25
Pig, 15Chicken, 48
Horse, 4 Escapee from prison, 2
The same data is presented below, but as an unranked bar chart. This time,
the area of their rectangular bar is proportional to the number of animals in
each category.
These kinds of chart are useful for presenting data sampled for
discontinuous variables, but sometimes the data is continuous. In such
cases a histogram is a better option.
Continuous data For variables such as height or weight that show a quantifiable change (a
change you can put a number to) the frequency table can be used to
produce a histogram. Consider the following table showing a distribution of
the number of male students and their heights in a class of AS biology
students.
Height Frequency 1.5 - 1.599 2 1.6 - 1.699 7 1.7 - 1.799 18 1.8 - 1.899 4 1.9 - 1.999 1
The independent variable now reflects a change in the heights of the
students from 1.5 meters up to 2 meters and the number of students falling
to specified height groups are tallied and counted. The “bar chart” formed is
now termed a histogram and the data shows the distribution of heights in
the student’s class.
25
15
48
42
0
5
10
15
20
25
30
35
40
45
50
Cow Pig Chicken Horse Escapee from prison
Frequency
This type of bell-shaped curve is called a normal distribution curve and forms
the basis of some slightly more complex statistical testing which you will
tackle later in the A2.
If you were to imagine and visualise this data, you would see that “most”
students are of average height with one very tall and two very short class
members. It is this ability to visualise a distribution in different ways which
makes this kind of data presentation a powerful tool in biology.
0
2
4
6
8
10
12
14
16
18
20
1.5 - 1.599 1.6 - 1.699 1.7 - 1.799 1.8 - 1.899 1.9 - 1.999
Fre
qu
en
cy
Height (meters)
16. The table shows the proportion of different bases in DNA extracted from four different species.
Adenine Cytosine Thymine Guanine Human 30.8 19.9
Chimpanzee 27.2 22.8 27.2 22.8 Shrew 26.7 23.3
(a) Fill in the missing data in the table [2]
(b) Compare the data of the shrew and the chimpanzee [2]
17. Smoking can impair lung function. An investigation was carried out
into the effect of smoking on lung function over 5 years. The peak flow
rate (a measure of lung function) is the maximum volume of air
expelled from the lungs in 60 seconds (dm3 min–1). Two female
volunteers, one a smoker (dashed line) and one a non-smoker (solid
line) were both aged 12 at the start of the study. They both had their
peak flow measured once a year for five years. The results are shown
on the graph below.
(a) Describe the data for the non-smoker. [1]
(b) Compare the data from the two volunteers. [3]
18. In 1978 the population of Elephant seals at Macquarie Island off the
coast of Antarctica was estimated at 140 000. It was thought that the
population had declined by 75% over the previous 10 years. In 1998 a
study estimated the island population to have recovered to 580 000.
(a) Calculate the estimated population of Elephant seals in 1968.
Show your working. [2]
200
250
300
350
0 1 2 3 4 5
Pe
ak f
low
(d
m3
/ m
in)
Time (years)
27.
Prophase Metaphase Anaphase Telophase
Number of cells 15 6
60- (15+9+30)
9 30
% of cells in stage 25 10
6 ÷ 60 x 100
15 50
30 ÷ 60 x 100
Degrees on pie chart 90 36 54
15% x 360
180
50% x 360
28. (a)
x-axis labelled correctly [1] y-axis labelled correctly [1]
points plotted correctly [1] line of best fit appropriately placed [1]
(b) As the sodium phosphate concentration increased from 0 to 0.1 mmol dm-3 the growth of the seedlings increased proportionally [1].
(c) Any one of ...
The line of best fit does not go through the origin. [1] When phosphate is not present, there is still some growth. [1] There is scatter about the line. [1]
(d) Any one of ...
More data points (particularly between 0.06 and 1). [1] Repeat several times and take the average. [1] Increase the length of time the seedlings grew. [1]
29. The replication rate (in cycles per week) is: B 10
Hours per week = 24 x 7 = 168
Number of cycles = 168 hours ÷ 16.8 = 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.02 0.04 0.06 0.08 0.1
Gro
wth
(m
m in
2 w
ee
ks)
Phosphate concentration (mmol dm-3)
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